Cyber-physical systems (CPSs) usually employ distributed sensor networks to gather, process and exchange information as a team. In contrast to the previous centralized secure state estimation (SSE) for CPSs, this paper proposes a distributed SSE algorithm via consensus-based distributed non-convex optimization protocols. The algorithm is implemented over a multi-agent network where each agent privately processes own sensing measurements while communicating with its neighbors via a graph topology. The combinatorial problem caused by the sparse sensor attacks is solved well via a transformation technique and a distributed vote location approach. Based on min-switching and check mechanisms, it is proved that the algorithm achieves consensus at the true system state with probability one under the condition of the graph being regular with a certain prescribed connectivity. Simulation results demonstrate the accuracy of the developed algorithm under the condition of attacks. (C) 2019 Elsevier Ltd. All rights reserved.